Modelling the flexoelectric effect in solids: A micromorphic approach
McBride AT, Davydov D, Steinmann P (2020)
Publication Type: Journal article
Publication year: 2020
Journal
Book Volume: 371
Article Number: 113320
DOI: 10.1016/j.cma.2020.113320
Abstract
Flexoelectricity is characterised by the coupling of the second gradient of the motion and the electrical field in a dielectric material. The presence of the second gradient is a significant obstacle to obtaining the approximate solution using conventional numerical methods, such as the finite element method, that typically require a C1-continuous approximation of the motion. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient contributions arising in this highly-nonlinear and coupled problem within a classical finite element setting. Our formulation accounts for all material and geometric nonlinearities, as well as the coupling between the mechanical, electrical and micromorphic fields. The highly-nonlinear system of governing equations is derived using the Dirichlet principle and approximately solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this intriguing effect that underpins or influences many important scientific and technical applications.
Authors with CRIS profile
Denis Davydov
Lehrstuhl für Technische Mechanik (LTM)
Paul Steinmann
Lehrstuhl für Technische Mechanik (LTM)
Involved external institutions
United Kingdom (GB)How to cite
APA:
McBride, A.T., Davydov, D., & Steinmann, P. (2020). Modelling the flexoelectric effect in solids: A micromorphic approach. Computer Methods in Applied Mechanics and Engineering, 371. https://doi.org/10.1016/j.cma.2020.113320
MLA:
McBride, A. T., Denis Davydov, and Paul Steinmann. "Modelling the flexoelectric effect in solids: A micromorphic approach." Computer Methods in Applied Mechanics and Engineering 371 (2020).
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